[ZeroFries]

I doubt most people have the desire to be productive mathematicians, which is as required to be a good mathematician as being 7' tall is for playing basketball (aka not actually required, but big help).

"Most people can be productive mathematicians, they just don't believe in themselves."

Most people can X if Y, where Y is not the usual case. Again, believing in yourself, having the desire to be great at something, etc, are all included in the extremely large set of factors which determine whether someone will be good at any given activity. To say a large portion of the population can be good at some activity, knowing full-while that they do not possess most of the helpful attributes, is disingenuous.